Сократить дроби: 1) (n^3 - nm^2)/(mn - n^2); 2) (36c - c^3)/(c^3 - 12c^2 + 36c); 3) (x^2 - 9x + 14)/(x^2 - 10x + 16). Сложить дроби: 4) 1/14x^2 - 1/21x^2y + 1/2xy^2; 5) (2 - 3y)/(y^2 - 9) - (5 - 2y)/(3 - y); 6) (2x + y)/(5x - y) + (3x - y)/(y - 5x).

1. $\frac{n^3 - nm^2}{mn - n^2} = \frac{n(n^2 - m^2)}{n(m - n)} = \frac{(n - m)(n + m)}{m - n} = \frac{-(m - n)(n + m)}{m - n} = -(n + m) = -n - m$ 2. $\frac{36c - c^3}{c^3 - 12c^2 + 36c} = \frac{c(36 - c^2)}{c(c^2 - 12c + 36)} = \frac{(6 - c)(6 + c)}{(c - 6)^2} = \frac{-(c - 6)(6 + c)}{(c - 6)^2} = -\frac{6 + c}{c - 6} = \frac{c + 6}{6 - c}$ 3. $\text{Допущение: в знаменателе опечатка, должно быть } x^2 - 10x + 16.$ $\frac{x^2 - 9x + 14}{x^2 - 10x + 16} = \frac{(x - 2)(x - 7)}{(x - 2)(x - 8)} = \frac{x - 7}{x - 8}$ 4. $\frac{1}{14x^2} - \frac{1}{21x^2y} + \frac{1}{2xy^2} = \frac{3y^2 - 2y + 21x}{42x^2y^2}$ 5. $\frac{2 - 3y}{y^2 - 9} - \frac{5 - 2y}{3 - y} = \frac{2 - 3y}{(y - 3)(y + 3)} + \frac{5 - 2y}{y - 3} = \frac{2 - 3y + (5 - 2y)(y + 3)}{(y - 3)(y + 3)} = \frac{2 - 3y + 5y + 15 - 2y^2 - 6y}{y^2 - 9} = \frac{-2y^2 - 4y + 17}{y^2 - 9}$ 6. $\frac{2x + y}{5x - y} + \frac{3x - y}{y - 5x} = \frac{2x + y}{5x - y} - \frac{3x - y}{5x - y} = \frac{2x + y - (3x - y)}{5x - y} = \frac{2x + y - 3x + y}{5x - y} = \frac{2y - x}{5x - y}$